共查询到20条相似文献,搜索用时 546 毫秒
1.
ABSTRACT We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators' domains and form domains. We obtain results valid for general Lipschitz domains, and stronger results for a special class of “almost convex” domains, which apply to domains with corners. 相似文献
2.
This paper contributes to the theory of uniform domains and Sobolev extension domains. We present new features of these domains and exhibit numerous relations among them. We examine two types of Sobolev extension domains, demonstrate their equivalence for bounded domains and generalize known sufficient geometric conditions for them. We observe that in the plane essentially all of these domains possess the trait that there is a quasiconformal self-homeomorphism of the extended plane which maps a given domain conformally onto a circle domain. We establish a geometric condition enjoyed by these plane domains which characterizes them among all quasicircle domains having no large and no small boundary components. 相似文献
3.
Tiberiu Dumitrescu 《代数通讯》2013,41(3):808-818
We study, under the name t-Schreier, the class of those integral domains whose group of t-invertible t-ideals satisfies the Riesz interpolation property. The so-called Prüfer v-multiplication domains (PVMDs) and Prüfer domains are special cases of t-Schreier domains. We show that, while a number of results known for Prüfer domains and PVMDs hold for these domains, the t-Schreier domains have a remarkable capability of unifying various results in that the results proved for t-Schreier domains can also be translated to results on pre-Schreier domains and hence on GCD and Bezout domains. 相似文献
4.
5.
本文研究了稍微广泛的一类Hartogs型域的自同构群.利用华域的自同构群,获得了一类有界对称域上的Hartogs型域的自同构群的具体形式,推广了有界对称域上的Hartogs型域的自同构群这一结果. 相似文献
6.
Makoto Sakai 《Complex Analysis and Operator Theory》2009,3(2):525-549
We discuss quadrature domains for subharmonic functions and prove the existence of core quadrature domains for certain positive
measures. The core quadrature domains are the smallest quadrature domains as measures and inherit good properties from quadrature
domains with finite volume. We next discuss new balayage for the class of harmonic functions integrable in a neighborhood
of ∞. We give several estimates of balayage measures. The new balayage is introduced to construct quadrature domains for harmonic
functions.
Submitted: June 26, 2008. Accepted: July 24, 2008. 相似文献
7.
Driss Nour El Abidine 《Annali dell'Universita di Ferrara》1990,36(1):175-183
In this paper, we are interested in a generalization of Nagata's theorem [13] to a new class of domains other than Krull domains,
the Mori domains and the PVMD domains (Theorem 1).
相似文献
8.
引入了相容半连续Domain、相容强连续Domain的概念,给出了一系列性质,讨论了相容半连续Domain、相容强连续Domain与相容连续Domain间的关系.引入了相容半Scott拓扑,并讨论了其相关性质. 相似文献
9.
Yoav Kallus 《Geometriae Dedicata》2014,173(1):177-184
We develop a theory of planar, origin-symmetric, convex domains that are inextensible with respect to lattice covering, that is, domains such that augmenting them in any way allows fewer domains to cover the same area. We show that origin-symmetric inextensible domains are exactly the origin-symmetric convex domains with a circle of outer billiard triangles. We address a conjecture by Genin and Tabachnikov about convex domains, not necessarily symmetric, with a circle of outer billiard triangles, and show that it follows immediately from a result of Sas. 相似文献
10.
We explore the key differences in the stability picture between extended systems on time-fixed and time-dependent spatial domains. As a paradigm, we take the complex Swift–Hohenberg equation, which is the simplest nonlinear model with a finite critical wavenumber, and use it to study dynamic pattern formation and evolution on time-dependent spatial domains in translationally invariant systems, i.e., when dilution effects are absent. In particular, we discuss the effects of a time-dependent domain on the stability of spatially homogeneous and spatially periodic base states, and explore its effects on the Eckhaus instability of periodic states. New equations describing the nonlinear evolution of the pattern wavenumber on time-dependent domains are derived, and the results compared with those on fixed domains. Pattern coarsening on time-dependent domains is contrasted with that on fixed domains with the help of the Cahn–Hilliard equation extended here to time-dependent domains. Parallel results for the evolution of the Benjamin–Feir instability on time-dependent domains are also given. 相似文献
11.
William E. Lang 《代数通讯》2013,41(12):5813-5836
Antimatter domains are defined to be the integral domains which do not have any atoms. It is proved that each integral domain can be em-bedded as a subring of some antimatter domain which is not a field. Any fragmented domain is an antimatter domain, but the converse fails in each positive Krull dimension. A detailed study is made of the passage of the“an-timatter”property between the partners within an overring extension. Special attention is given to characterizing antimatter domains in classes of valuation domains, pseudo-valuation domains, and various types of pullbacks. 相似文献
12.
In this paper, we discuss the Cauchy-type integral formula of hypermonogenic functions on unbounded domains in real Clifford analysis, then we extend the Plemelj formula and Cauchy–Pompeiu formula of hypermonogenic functions on bounded domains to unbounded domains. We also deal with the Green-type formula on unbounded domains and get several important corollaries. 相似文献
13.
Maria-Magdalena Boureanu Alejandro Vélez-Santiago 《Journal of Differential Equations》2019,266(12):8164-8232
We investigate a class of quasi-linear elliptic and parabolic anisotropic problems with variable exponents over a general class of bounded non-smooth domains, which may include non-Lipschitz domains, such as domains with fractal boundary and rough domains. We obtain solvability and global regularity results for both the elliptic and parabolic Robin problem. Some a priori estimates, as well as fine properties for the corresponding nonlinear semigroups, are established. As a consequence, we generalize the global regularity theory for the Robin problem over non-smooth domains by extending it for the first time to the variable exponent case, and furthermore, to the anisotropic variable exponent case. 相似文献
14.
Alice Fabbri 《Journal of Pure and Applied Algebra》2011,215(5):1069-1084
We study the class of integrally closed domains having a unique Kronecker function ring, or equivalently, domains in which the completion (or b-operation) is the only e.a.b star operation of finite type. Such domains are a generalization of Prüfer domains and have fairly simple sets of valuation overrings. We give characterizations by studying valuation overrings and integral closure of finitely generated ideals. We provide new examples of such domains and show that for several well-known classes of integral domains the property of having a unique Kronecker function ring makes them fall into the class of Prüfer domains. 相似文献
15.
Björn Ivarsson 《Arkiv f?r Matematik》2002,40(2):275-300
We give interior estimates for first derivatives of solutions to a type of complex Monge-Ampère equations in convex domains.
We also show global estimates for first derivatives of solutions in arbitrary domains. These global estimates are then used
to show interior regularity of solutions to the complex Monge-Ampère equations in hyperconvex domains having a bounded exhaustion
function which is globally Lipschitz. Finally we give examples of domains which have such an exhaustion function and domains
which do not.
The author was partially supported by the Royal Swedish Academy of Sciences, Gustaf Sigurd Magnuson’s fund. 相似文献
16.
Hua’s theory of harmonic functions on classical domains is generalized to the theory on holomorphic vector bundles over classical
domains and further on vector bundles over the real classical domains and quaternion classical domains. In case of the simplest
quaternion classical domain there is a relation between Hua operator and Dirac operator, by which an AdS/CFT correspondence
of Dirac fields is established. 相似文献
17.
This paper derives general analytical formulae for the conformal maps from multiply connected circular preimage domains to
multiply connected quadrature domains by considering the Bergman kernel functions of the preimage and target domains. The
new formulae are expressed in terms of the Schottky–Klein prime function. They generalize, to the case of arbitrary connectivity,
a formula relevant to doubly connected domains derived by Y. Avci in 1977.
Submitted: September 17, 2007. Accepted: June 5, 2008. 相似文献
18.
Xiaotao Huang Dongsheng Li Lihe Wang 《Journal of Mathematical Analysis and Applications》2011,376(2):443-450
In this paper, we investigate the symmetry of domains and solutions of integral equation systems on bounded domains. Under some natural integrability conditions, we prove that the domains are balls, all positive solutions of systems are radially symmetric and monotone decreasing with respect to the radius. 相似文献
19.
A.O. Çelebi 《复变函数与椭圆型方程》2015,60(4):566-582
The Schwarz problem for bi-analytic functions in unbounded circular multiply connected domains is considered. We combine constructive methods applied to boundary value problems for complex partial differential equations in simply connected domains and for the Riemann–Hilbert type problems in multiply connected domains. A general method is outlined and the case of doubly connected domains is discussed in details. Solution is obtained in the form of a series. 相似文献
20.
Ciprian G. Gal Mahamadi Warma 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2016,67(4):83
We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction–diffusion equation on non-smooth domains subject to nonlocal Robin boundary conditions, characterized by the presence of fractional diffusion on the boundary. Our results are of general character and apply to a large class of irregular domains, including domains whose boundary is Hölder continuous and domains which have fractal-like geometry. In addition to recovering most of the existing results on existence, regularity, uniqueness, stability, attractor existence, and dimension, for the well-known reaction–diffusion equation in smooth domains, the framework we develop also makes possible a number of new results for all diffusion models in other non-smooth settings. 相似文献